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What is the unit vector in the direction of v = (3, 4)?
What is the unit vector in the direction of v = (3, 4)?
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Practice Questions
1 question
Q1
What is the unit vector in the direction of v = (3, 4)?
(0.6, 0.8)
(1, 1)
(3, 4)
(0, 0)
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Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)
Questions & Step-by-step Solutions
1 item
Q
Q: What is the unit vector in the direction of v = (3, 4)?
Solution:
Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)
Steps: 6
Show Steps
Step 1: Identify the vector v, which is given as (3, 4).
Step 2: Calculate the magnitude (length) of the vector v using the formula |v| = √(x^2 + y^2), where x = 3 and y = 4.
Step 3: Substitute the values into the formula: |v| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Step 4: To find the unit vector, divide each component of the vector v by its magnitude: unit vector = v / |v|.
Step 5: Perform the division: unit vector = (3/5, 4/5).
Step 6: Simplify the fractions: unit vector = (0.6, 0.8).
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